Enhanced beam director with improved optics

ABSTRACT

A beam director for use in 3D printers comprises a first mirror rotating about its longitudinal axis for redirecting a beam onto a second mirror and then onto a work surface, which may result in a beam with a distorted shape. A beam corrector, e.g. a lens or a reflective surface, is used to ensure the beam has the same desired dimensions in the first and second perpendicular direction when striking the work surface.

APPLICATION

This application incorporates by reference and claims priority to andthe benefit of, US Provisional Patent Application Ser. No. 62/981,128with filing or 371(c) date of Feb. 25, 2020.

TECHNICAL FIELD

The present invention relates to a beam director, and in particular to abeam director for a 3D printer including a first rotating reflector anda second rotating annular reflector.

BACKGROUND

A beam director for use in 2D and 3D printers, such as the one disclosedin U.S. Pat. Nos. 9,435,998, 10,416,444 and 10,473,915, which areincorporated herein by reference, comprises a first mirror rotatingabout its longitudinal axis, with a reflective surface at an acute angleto the longitudinal axis. Accordingly, a beam transmitted along thelongitudinal axis may be redirected onto a second mirror, and then to awork surface, which is typically perpendicular to the longitudinal axis.

SUMMARY

The present invention relates to a beam director comprising:

a rotatable first reflector rotatable about a longitudinal axis forreceiving a beam from a beam source along the longitudinal axis, thefirst reflector including a reflective surface at an acute angle to thelongitudinal axis for reflecting the beam;

an actuator for rotating the first reflector about the longitudinalaxis, whereby the first reflector rotates and reflects the beam at aconstant angle to the longitudinal axis;

a second annular reflector rotated by the actuator and rotating in acircle around the longitudinal axis of first reflector as firstreflector rotates; constantly facing the first reflector at a constantangle; the second reflector further configured to reflect the beamtowards a work surface at a constant angle thereto,

Accordingly, an object of the present invention is to address theoptical components for handling the beam of the prior art by providingcorrective elements, whereby the beam has the same dimension in thefirst and second directions when incident on the work surface or whenthe beam keeps the proportion between the first and second directionswhen incident on the work surface. Where the first direction and thesecond direction are the local beam coordinates denoted by lower case xand y cartesian coordinates system.

Surfaces can be expressed in many ways. One way we'll be using in thisapplication is to define a surface by two orthogonal curvature lines Cx13 and Cy 14 where their vertices meet at the optical Axis FIG. 8. We'llbe also applying other ways to define a surface.

Yet, another aspect of this invention is to control the beam to comeinto focus on both x and y dimensions on the work surface.

Another aspect of the invention is to control the beam size on both xand y at the print surface,

Yet, another aspect of the invention is to focus a non symmetricalsource beam such as a rectangle source.

Another aspect of this invention is to control the beam to come intofocus on one dimension. Either the x or the y dimension. Such featurescan be used to control the pixel logical size 25 by 25 were pixellogical size composed of moving physical pixel size and it can beexpressed by:

Logical_Pixel_size [mm{circumflex over ( )}2]=physical_pixel_size[mm]*Vb [mm/sec]*T [sec]

Where Vb is the moving beam speed and Tp the time traveling over alogical pixel. Additionally when using a single mode beam or a fiberlaser with small clade diameter then the desired beam size may be largerthan the smallest focal beam size of the single mode laser or a fiber.Therefore, the beam size at the work surface needs to be adjusted.

The second reflector may take the form of a rotating reflector or astationary arcuate reflector, which is used to reflect the beam alongstraight or arcuate paths on the work surface. We'll analyse thestationary second reflector, however, all analysis applied also to aphysically rotated second reflector as well. When applying the analysisto a rotating physical second reflector then a vertical slice is cutfrom the stationary reflector to be used as the physically rotatedsecond reflector.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1. Is an isometric view of a prior Art of beam director system

FIG. 2. Prior Art view of a beam director system with two coordinatessystem; beam local coordinates and global coordinates

FIG. 3. Is an isometric view of a Beam director with collimated beamsource using a cone second reflector (Prior Art)

FIG. 4. Illustration of Collimated beam source

FIG. 5. Beam shape and size at the work surface for Collimated beaminput using FIG. 3 system.

FIG. 6. Isometric view of a beam director system including a beam sourcewith local and global coordinate systems.

FIG. 7. Side view of a beam director system including a beam source

FIG. 8. Illustrates M1 mirror with the surface curvatures

FIG. 9. An isometric view of the M1, M2 focusing a beam source on to thework surface

FIG. 9A. Side view of FIG. 9 where the beam source is collimated

FIG. 9B. Side view of M1, M2 focusing system where the beam source isdiverging

FIG. 9C. Side view of M1, M2 focusing system where the beam source isdiverging where M1 is collimating the source beam

FIG. 9D. Side view of the M1, M2 system wnere M1 and M2 converging thecollimated source beam

FIG. 10. Isometric system for toroidal M2 surface M2 focusing a rotatingbeam

FIG. 11. A side view of FIG. 10 system

FIG. 12 Implementation of FIG. 10 with an additional rotating mirrorinstead of rotating light source

FIG. 13. Diverging beam source

FIG. 14. Desired Beam shape and size at the work surface for the inputbeam in FIG. 13.

FIG. 15. Focused narrow beam on the x direction showing x and y relativedimensions

FIG. 16 Logical pixel is composed from moving FIG. 15

FIG. 17. Focusing a diverging beam with off axis matching parabolas.

FIG. 18. An equivalent lens optics system on the x dimension.

FIG. 19. A ray tracing analysis for the y dimension when using acylindrical lens.

FIG. 20. Selecting the M2 surface from an off axis toroidal.

FIG. 21. Analysis of a parabolic M2 in an M1 & M2 system.

FIG. 22A M1, M2 construction and placement.

FIG. 22B. Pitch of M1 around the Y axis

FIG. 23. Focused beam sample

FIG. 24. M1 biconic with flat M2

FIG. 24B. Beam output from the system in FIG. 24.

FIG. 25. M1, M2 constructed away from the work surface

FIG. 26. M1, M2 construction when M1 is pushed back in relation to M2

FIG. 27 M1 & M2 constructed from the same parabolic properties

FIG. 28 Alternative and practical setting for M1 & M2 for FIG. 27

DETAILED DESCRIPTION

The objective of this invention is to provide solutions to focusing andcontrolling the beam size at the work surface in a Beam Director System.

Glossaries and Definitions

The glossaries and definition will help a skilled in the art understandthe terms and methods used in this application. More opticalclarification and properties can be found in Optical System Design, byRobert E. Fischer Second Edition.

Asp—Aspherical value in defining surfaces defining departure from aspherical profile. curvature—C curvature is the reciprocal of R theradius.

curvatures of surfaces—Cx 13 and Cy 14 as shown in FIG. 8 are orthogonalcurvatures defining a surface where Cx and Cy where the vertexcurvatures meet at the optical axis as shown in FIG. 8. Beam—Beam oflight. Beam Parameter Product

(BPP)—Is the product of a laser beam's divergence angle (half-angle) andthe radius of the beam at its narrowest point.

Lower case x,y and z coordinates—denotes local beam coordinates:

In this application we define a lower case x,y and z coordinate systemthat is cartesian coordinates that are local to the beam. Lower case zdenotes the direction of the beam while x and y denotes the beam size.Therefore, any reference to lower case x,y or z axis will be referringto local coordinates of the beam along the optical axis 3. Where z isalso is the optical axis. x0, y0—is the starting coordinates of a beamin a system where the beam is bounced from surface to surface.

surface function—is defined by a 2D function that is rotated around theZ axis or around a parallel axis to the Z axis. xn, xn—is the n surfacecoordinate of the beam starting from the beam source where x0, y0 is thesource beam, x1, y1 is the first surface in the beam path and so on.xfinal, yfinal—are the last surface coordinate of the beam. LogicalPixel—is a pixel composed of a moving physical beam where the loggalpixel size is controlled by the moving speed and the activation time ofthe physical beam. Lower case coordinates denote also local coordinatesfor surface construction formulas.

M1 4 and M2 2 are the first and second mirror respectively. FlatM1—referred to flat surface mirror.

Flat M2—Using cone surface where M2 surface function is defined as a 2Dsurface function of y=x−R0 rotating around the Y axis where R0 is theRadius of the cone at the base. Flat M2 also referred to as cone M2.

Physically rotated reflector—is a rotator that is physically rotatedabout a rotational axis. As the physical rotated reflector rotates it isfacing the first reflector, therefore reflecting the beam received fromthe first rotator and reflects the beam to the work surface.

Optical distance—a distance measured by summing the total optical pathfrom starting point to ending point along the optical axis.

Units—Although, this doc will be using mm units. It could be either ininches or any other units or multipliers when using multipliers then allunit dimensions need to be corrected by the same multiplier. Upper caseX,Y and Z denotes global system coordinates as shown in FIGS. 1, 2, 6,and 7. WFE—Wave front error. This quantity is computed from each raytrace and it used to represent the delay between ray start and rayfinish surfaces. The total root-mean-square WFE is calculated from thedeviations in WFE within each group of rays.

A beam source 5 may be configured to generate a beam of light, which iscollimated, non collimated or non symmetrical, such as rectangle-likeshape.

The following sections cover the various solutions based on a stationaryM2 reflector 2. The same solution applies for a physically rotating M2reflector, where a small section of the M2 reflector is implementing thesame surface formula and analysis as in the non rotating M2 reflector.When referring to the M1 or M2 reflectors, the disclosure is referringto a first reflector surface 4 or the second reflector surface 2respectively.

The M2 reflector may be an annular structure where each point on thesurface encircles the optical Z Axis 9. Mathematically, any point on thesurface circling the optical Z axis 9 may be at the same distance to theoptical Z Axis 9. Conceptually, if we slice the annular structuresurface into an unlimited number of slices, then each slice may be acircle where the optical axis Z 9 is at the center.

The M2 surface function may hereby be defined by a 2D function that isrotated around the Z axis or around parallel to the Z axis. As anexample y=a*x is a linear function y(x) representing a cone structurewhen y(x) is rotated around the z axis where a is the tangent of thecone half angle.

Conic sections are surface functions as they defined as follows:

mathematical curves (parabolas, hyperbolas, circles, etc.) that satisfyquadratic algebraic expressions (See Optical System Design, Robert E.Fischer Second Edition, Chapter 7 Page 117). Geometrically, they areequivalent to the intersection of a cone with a plane, hence the name.When a conic section is rotated about an axis, it sweeps out a surfacein three dimensions (paraboloid, hyperboloid, sphere or ellipsoid).Surfaces of this type are very useful in optics and defined by thefollowing equation in the Vertex origin Cartesian coords:

z(r)=C·r ²/(1+√{square root over (1−(1+Asph)·C ² ·r ²))}

-   -   Where: r²=x²+y²        where:        C: is the curvature of a surface: positive for a surface curving        towards +z, and negative if curving towards −z. 0 (Zero)        curvature is a flat surface (as the radius is 1/C for a flat        surface the radius is infinite).        Asph or Asp dictates the surface classification as Asp defined        as a departure from a sphere. Asp with a 0 value specifies a        sphere. As an example, the Asp value of −1 specifies a        paraboloid, −1<Asp<0 specifies prolate ellipsoid, Asp>0        specifies oblate ellipsoid, and Asp<−1 specifies hyperboloid.

Similarly, z(r) the surface function may be expended representingpolynomial coefficients as well to fulfill the imposed conditions.

z(r)=C·r ²/(1+√{square root over (1−(Asph+1)·C ² ·r ²))}+A ₁ ·r+A ₂ ·r² + . . . +A _(j) ·r ^(j)

This function provides a greater level of flexibility whereas an examplesetting C=0 and all coefficients to 0 but A1 creates a cone structure.

A toric surface is the surface swept out when a function z(y) below isrotated about an axis that is parallel to the y axis. This surfacefunction can be zero, circular conic, or include polynomial terms.

z(y)=C·y ²/(1+√{square root over (1−(Asph+1)·C ² ·y ²))}+A ₁ ·y+A ₂ ·y² + . . . +A ₁₄ ·y ¹⁴

When this z(y) curve is revolved about an axis parallel to the local yaxis, the resulting

toric surface is exactly circular in its xz plane, and is exactly thespecified function in theyz plane. In this document when referring to toric surface C will bemarked Cx′ where Cx′ is the reciprocal of the radius in the xz plane towhich it is positive if bending towards +z or negative if bendingtowards −z.x,y, and z are all measured with respect to the vertex and are orientedso that z lies normal to the surface at its vertex.

When tilting a surface it is about the x axis when pitching a surface itis about its y axis.

Please also note: biconic surface is a surface with an additional degreeof flexibility where the spherical component of a toric is asphericalwhere Cx and Cy curvature are aspherical and use AspX and AspY toquantify the departure from aspherity. when the AspX or AspY is zerothen a toric surface is formed.

When referring to the M1, M2 surface in this application, the reflectorM2 2 will be mostly defined by a toric function while reflector M1 withbiconic. When M2 and M1 presenting the same family such as parabola thenboth can be represented with the same system.

Additionally or alternatively, only polynomials may be used for thecomplete definition of the surface 2 while imposing the requiredspecifications.

z(r)=A ₀ ·r ⁰ +A ₁ ·r ¹ +A ₂ ·r ² +A ₃ ·r ³ + . . . +A _(j) ·r ^(j)

Polynomial terms are useful on their own, without curvature orasphericity, in polynomial optics such as Schmidt correctors. More oftenthey are combined with curvature and asphericity to provide smallhigh-order corrections to a surface.

Usually, only the first few even coefficients are sufficient as A2, A4,and A6 since most optical surfaces will be very nearly approximated bythe conic aspheric profile.

z(r)=C·r ²/(1+√{square root over (1−(Asph+1)·C ² ·r ²)}+A ₂ ·r+A ₄ ·r⁴ + . . . +A _(j) ·r ^(j)

When the light beam 3 transmitted by the beam source 5 is collimatedthen the first M1 reflector 4 may be a flat mirror whereby the second M2reflector 2 may be performing the focus of the beam 3 as in FIGS. 9 &9A. The second M2 reflector surface 2 may be changing the strikingcollimated beam 3 to a non collimated beam where the x & y dimension ofthe beam is converging into focus or a desired dimension.

In another aspect of the invention, when a collimated beam 3 strikes thefirst M1 reflector 4. When the first M1 reflector 4 is flat, the firstM1 reflector 4 may be changing the beam moving direction from the Z axis9 to rotational about the Z axis 9 while keeping the beam collimated.Preferably, a 45° angle between the beam source optical axis 9 to thefirst M1 reflector surface 2 as shown in FIG. 7. A non flat second M2reflector 2 may be changing x in a nonlinear correlation when a linearcorrelation refers to the standard thin lens formula.

With reference to FIG. 7, when the first M1 reflector 4 is flat, thefirst M1 reflector 4 keeps local x,y beam components in tack. The secondM2 reflector 2 may include an annular, e.g. cone, structure configuredto change the x component by definition as it will bring into focus thex component in a distance of about R, where R is the distance 11 and mayalso be equal to the distance 12 when the second M2 reflector 2 isconical, from the optical axis 9 of the beam source 5 and/or the firstM1 reflector 4 to the second M2 reflector 2 when the cone is constructedwith a linear line of about 45°.

Using the conical surface for the second M2 reflector surface 2, thefunction may be defined as a 2D surface function of y=x−R0 rotatingaround the y axis where R0 is the Radius of the cone at the base. Thisfunction as shown in U.S. Pat. No. 10,416,444 can correct the beam sizeto be the same in both dimensions at a predetermined distance to thework surface.

Relating to the cone structure in FIG. 3 (Prior Art). One way to focusthe beam is by using a cylindrical lens on the y component of the beamwith focal point Fy where fy is larger than 2*R and position at anoptical distance Fy from the work surface 7. Although Fy can havemultiple values larger than 2*R, it is recommended to use a value closerto 2R. This will ensure that the beam in the x and y dimensions arediverging or converging in about the same rate. As an example selectinga cylindrical lens Fy of 5/4*R and positioned at a distance of %*R fromM1 is a sound solution using U.S. Pat. No. 1,046,444.

When using a laser source with BPP that enables (the lower the BPP thebetter) focus to a smallest beam size of WO in diameter. Where theprovided beam source is collimated with a beam diameter size 2*ho (e.g.5 mm for a 10 mm beam diameter) and a BPP sufficient to bring the beamto small focus WO of (e.g. 2 um when using a single mode laser).

Using cone structure M2 as in FIG. 3. A Logical Pixel LP can beconstructed from the WO physical pixel using any one of the followingmethods:

Solve by Adding Cylindrical Lens Method

The first M1 reflector 4 may not be part of the calculation when it is aflat mirror. Therefore, a cylindrical lens may be placed before thefirst M1 reflector 4 or after the first M1 reflector 4. Preferablybefore the first M1 reflector 4, otherwise a larger circular surfacelens, as well as a rotating first M1 reflector 4 may be needed. Thesecond M2 reflector 2 in the shape of a cone focuses the x component ofthe beam 3 at a distance R from the second M2 reflector 2. To create thedesired LP the work surface 1 should be placed away from the focal pointeither before or after the focal point f. FIG. 18 shows an equivalentoptic mirror for the second M2 reflector 16 for the x axis where thefocal point Fx is placed at a distance R 13 from the second M2 reflector16. hox 18 is the x component of the collimated beam source. hix 15 isthe x component of the image of the at the work surface 7. Similarly,the cylindrical lens equivalent system is shown in FIG. 19 where theyaxis component is resolved to an image hoy 22 where the source beam ycomponent 21 is striking the cylindrical lens 24 with focal lens 19placed at an optical distance greater than 2R from the work surface 7.The beam source 5 is placed at a distance 23 from lens 24.

Hix 15 and hiy may be equal at the work surface 7. For the x axis raytracing dimensions are is resolved by:

-   -   (1) hix=hi    -   (2) Fx=R    -   (3) hox=ho    -   (4) Fx/Lx=hox/hix

Lx=Fx*hix/hox=R*hi/ho

Similarly for the y ray tracing is resolved by:

-   -   (1) hiy=hi    -   (2) Fy=2.25 R    -   (3) hoy=ho    -   (4) Fx/Ly=hoy/hiy

Ly=Fx*hiy/hoy=2.25*R*hi/ho

Where Lx 14 is the distance from the Fx point to point where we producethe desired LP in the x dimension and where the work surface 7 is to beplaced. Similarly, Ly 20 is the distance from the Fy focal point to thework surface 7.

As an example, when R is 125 mm, ho is 5 mm, and where the desired LP is50 urn:

-   hi=0.5*LP→0.025 mm; ho is the radius    -   Lx=125*0.025/5=0.625 mm    -   Ly=2.25*125*0.025/5=1.4 mm

A logical Pixel LP of 50 um was created by adding a cylindrical lens 24and positioning it between the beam source 5 and the first M1 reflector4.

Logical pixel LP can also be created without a cylindrical lens where amoving rectangle can create a square like LP as shown in FIGS. 15 and 16where a narrow rectangle 26 by height 27 can generate a square with alength side 25. As an example when using a single mode laser that isable to focus to 2 um. The LP (e.g. 50 um) may be constructed bycontrolling the scanning speed controlling the pixel speed over an areawhere. The cone structure at the focus point will be producing arectangular beam, where yfinal is 50 micrometer xfinal is 2 micrometer(from the cone).

As the scanning is performed with the first M1 reflector 4 rotating. Thelogical beam diameter is constructed with the control of Vm speed at thefirst M1 reflector 4 calculated as 2*π*R1. Tp is the on time to producethe logical pixel and T is the rotation period where f=1/T.

-   -   (1) Vm=2*π*R*f is M1 rotations/sec    -   (2) Lp=Vm*Tp

Tp=LP/(2*π*R*f)

To continue with the same example where required LP is 50 um and WO of 2um where f is 1 rotation/sec. The on time to generate the Lp is:

Tp=0.050/(0.002*125*π*1)=63 milliseconds

Please also note that any increase in laser speed may also call for anincrease in the laser power to keep the absorbed surface energyconstant.

A controller may turn the pixel on for the duration of Tp. This willproduce a symmetrical logical pixel where LP=Vm*Tp.

In another aspect of the invention, the beam 3 does not have to be inperfect collimation. In such a case the thin lens formula will beutilized for both to match the desired x and y dimension at the worksurface 7:

1/fx=1/sox+1/six

1/fy=1/soy+1/siy

Where Fx is the focal point for the x dimension, sox is the objectdistance to the equivalent lens and six is the image distance to theequivalent lens. Similarly, for the x dimension sox is the objectdistance to the equivalent lens and six is the image distance to theequivalent lens.

In another aspect of the invention a lens may be placed between thefirst M1 reflector 4 and the second M2 reflector 2. In this case thelens will be annular to cover the rotating beam span.

In this method, the function of the second M2 reflector surface 2 isperforming correction to bring the beam 3 into focus at the work surface7.

Additionally, The first M1 reflector 4 changes the local x,y beamcomponents where the second M2 reflector 2 is completing the Opticalcorrection.

Geometrical Design of the Toroidal Mirror using M2 flat mirror

FIG. 12, presents the design parameters of the corresponding toroidalmirror for focusing the light beam 3 from the beam source 5.

Here are some of the design considerations:

FIG. 12. represents a two-mirror configuration where the second M2reflector is toroidal and where the first M1 reflector 4 is flat. Thissystem will be using x′y′z′ coordinates. where the x′ axis is directedtoward the observer.

Light 3 from a beam source 8, preferably a fiber laser, is directedalong the rotation axis 9 toward the first M1 reflector, 4 which may betilted at 45° to the rotation axis 9 and/or the z axis, and rotates inabout the z′ axis. The beam source 5 is placed at a distance h 10 fromthe first M1 reflector 4 along the optical axis 9 which is also the M1rotational axis. The striking beam 3 may then reflect from the first M1reflector 4 to the second M2 reflector 2 in parallel to the y′ axis bystriking the toroidal M2 mirror and reflecting from the second M2reflector 2 in parallel to the z′ axis which is also the rotational axis9. d 11 is the distance between the rotational axis z′ and the reflectedbeam from M2.

C1 28 is the center of the toroidal mirror in the y′z′ plane (tangentialplane), C2 29 is the center of the toroidal mirror in the x′y′ plane(sagittal plane), V 30 is the vertex of the toroidal mirror. The radiiof the mirror are: C1−V=R′ (tangential plain) and C2−V=r (sagittalplane). Angle between the beam reflection point at the second M2reflector surface 2 and C1 and the vertex V on the x′y′ plane V may be0=45°.

C2 is on the rotation axis.

The second M2 reflector equation is given as:

$\begin{matrix}{{{\frac{1}{p} + \frac{1}{q_{T}}} = \frac{2}{R^{\prime}\;\cos\;\theta}}{{\frac{1}{p} + \frac{1}{q_{S}}} = \frac{2\cos\;\theta}{r^{\prime}}}} & (1)\end{matrix}$

where p=h+d is the object distance, q_(T) is the image distance intangential plain (from reflection point at mirror M2 to I₁ 31 point) andq_(s) is the image distance in sagittal plane (from reflection point atmirror M2 to I₂ 32 point). In order to have image in both plains at thesame distance we impose: q_(T)=q_(s)=q, or equivalently:

$\begin{matrix}{\frac{1}{R^{\prime}\;\cos\;\theta} = {\left. \frac{\cos\;\theta}{r^{\prime}}\Rightarrow r^{\prime} \right. = {R^{\prime}\;\cos^{2}\theta}}} & (2)\end{matrix}$

Furthermore, in order to eliminate the aberration (the smallest imagesize) p=q must is imposed:

p=q=R′ cos θ.  (3)

From the geometry presented in FIG. 12 we get:

C ₁ C ₂ +d=R′ cos θ

R−r′+d=R′ cos θ  (4)

Combining equations (2) and (4) resulted in:

$\begin{matrix}{{R^{\prime} - {R^{\prime}\cos^{2}\theta} + d} = {\left. {R^{\prime}\cos\;\theta}\Rightarrow R^{\prime} \right. = \frac{d}{{\cos\;\theta} - {\sin^{2}\theta}}}} & (5)\end{matrix}$

As an example for d=125 mm and 0=45° we get R′=603.5534 mm andr′=301.7767 mm using equation (2). The object distance according toequation (3) is p=h+d=R′ cos(0). Therefore, the distance from the beamsource 5 to the rotating flat first M1 reflector is h=301.7767 mm. Theimage of the beam source facet according to equation (3) positioned atthe distance q=426.7767 mm, so as R′ sin(e)=426.7767 mm, the image, orthe working surface 7 is positioned at the main axis (at the line C1−V)of the second reflector 2.

Alternatively, the beam source 3 may come from below into a rotatingfirst M1 reflector 4 about the Y axis, where the first M1 reflector 4may be tilted in 45° from the Z axis.

Another aspect of the invention is to use a rotating beam source 8directed at a toroidal second reflector 2, see FIGS. 10, 11 and 20. Whenthe light source 8 is rotating and diverging towards the second M2reflector surface 2, where the second M2 reflector 2 is toroidal-shapedand defined by Cx, Cy and an off-axis portion is to be used. The surface2 may be created with Cx′=−0.00165, C=−0.0033 where Cx′ is defined onthe XY plane and C is the curve that is swept around the Y axis. Where aselection of |C|=2|Cx′| ensured to bring the beam into focus. Theselected surface 2 to use is the off-axis surface at Y ˜428 mm where thebeam source 8 will be rotating around the Y axis. Another aspect of thisembodiment is to replace the beam source 8 with a rotating first M1reflector, and have the beam source 8 traveling down towards a 45° intothe first M1 reflector 4.

Another aspect of the invention is to use two paraboloids surfaces forthe first M1 reflector 4 and the second M2 reflector 2, where the firstM1 reflector 4 and the second M2 reflector 2 are identical paraboloids.The expanding beam 3 may be collimated after departing from the first M1reflector 4. The second M2 reflector may be converging the parallel beamback to its source as in FIG. 17. The first M1 reflector 4 may bepositioned so it will collimate the light coming to the second M2reflector 2, where the second M2 reflector 2 will bring the light intofocus.

Another preferred aspect of the invention is when the first M1 reflector4 and the second M2 reflector 2 performing the focus functions for anexpanding beam where the second M2 reflector 2 may comprise a paraboloidand the first M1 reflector 4 may comprise a surface where one dimensionis defined by sphere (Cx curvature, more below) and the orthogonaldimension is an aspheric (C with aspheric value) additionally the firstM1 reflector surface may be pitched in about 45° degrees. See FIG. 9C &FIG. 8. In this case the second M2 reflector 2 may comprise a paraboloidand the first M1 reflector 4 may be a swept Cx′ 34 around a parallelline to the y axis where its curve may be defined by curve C 35 withAspheric value of ˜−0.5. C˜2*Cx′ (C curvature is equal to about twotimes Cx′ curvature) as this surface is rotated by ˜45° degrees about aparallel to the y axis as shown in FIGS. 22A & 22B.

The first M1 surface 4 is positioned around the focal point location ofthe second M2 reflector 2 paraboloid where its optical axis coincideswith the paraboloid. Using the vertex cartesian coordinates:

z(y)=C·y ²/(1+√{square root over (1−S·C ² ·y ²))}

Where S=0 (as Asp=−1)→z(y)=C·y²/2

Also z(y)=1/(4*P)*y²→C=½ *P where P 38 is the focal of the parabola

The placement of the first M1 reflector 4 and the second M2 reflector 2is shown in FIG. 21, where the first M1 reflector 4 is placed at adistance of 110 from the vertex of the second M2 reflector 2, where theoptical axis of the first reflector 4, and the paraboloids centercoincide. I is about a distance P where P is the focal point of thesecond M2 reflector 2 (e.g. the second M2 reflector 2 may comprise aparaboloid, a rotating parabola wherein the parabola vertex 33 is at theorigin of the XZ plane). Setting I=I2+I3 or about equal to will reducethe number of parameters needed where I2 12 and I3 11. The constructingparabola and location is shown in FIG. 21 and it can be expressed:

½*C*y ²=½*(½*P)*y ² ;C is Paraboloid

curvature where C=1/(2P) Or P=Rc/2 as Rc=1/C

This solution is based on finding matching surfaces. As there arenumerous surfaces there is a need to match the surfaces with theopposite function if there is a need to correct a beam as an example.

In this case the beam is deflected from the first M1 reflector surface 4with focus function imposed by the first M1 reflector surface 4. As itis facing an annular ring from the paraboloid its function should bebased on a curvature as well.

As an example let's assume that we like to get a focused beam on thework area the beam with a radius R=100 mm when M1 is rotating. Theparaboloid to use may have a focal point P at around R/2→50 mm. C for M2is 1/(2P)→0.01. Set C for M1˜−C of M2. C for M1 −0.01

Set Cx for M1 about equal to % of C M1 (because of the M2 45 degreespitch).

Set C for M2 to −C of M1. Set the pitch angle to −45 degrees for M1. setAspheric value to −0.5 for M1 and −1 for M2. Set M2 Z location to be ataround the focal point. Set the expanding beam source at a distance tocover the desired M1 diameter (d=d0+L*Na) beam source. Set the beam goaleither as WFE or to minimum beam final size target when using Zemax orany equivalent optics software to fine tune C(M1) C(M2), Cx(M1) ASP alsoset the pitch angle as 45.74°. Please note: some software will have moredegree of freedom. Therefore, this is a suggested starting parametersThe following values are fine tuned:

-   -   C for M1=0.01; set to fixed    -   C for M2=−0.01043 (from −0.01)    -   Cx (belongs to M1)=−0.0049 (from −0.5)    -   Asp for M1=−0.45 (from −0.5)    -   M1 distance to M2 vertex z distance=50.79 (from 50)

The focused beam shown in FIG. 23 is 105 urn reflecting a fiber opticsource input of 105 um.

Setting another fix setting (set ASP to fixed −0.5 or C for M2 or pitch)is producing another set of working values with the same size outputbeam.

Another way to design the surface is by simply using existing surfacesand scale it.

Let's say that we want an arc with a radius of 250 mm and not 100. Thenwe adjust all dimensions proportionally:

-   C for M1=0.01; set to fixed→0.01*⅖→0.004-   C for M2=−0.01043 (from −0.01)→0.004172-   Cx (belongs to M1)=−0.0049 (from −0.5)→−0.00196-   Asp for M1=−0.45 (from −0.5); Pure number no change-   M1 distance to M2 vertex z distance=50.79 (from    50)→5/2*50.79→126.975

Another aspect of the invention is to set the focal parameter so it willgenerate a focus in one direction therefore generating a longrectangular like line. This line can be used as a physical pixel whereit will generate a logical pixel as shown in FIG. 16.

Yet, another aspect of the invention is to keep expanding the beam afterthe first M1 reflector as in FIG. 25. This will create a longer focalpoint for the system. Therefore, the beam director will be far from thework surface 7 as the bulk of the fousing function is done by theparaboloid second M2 reflector 2. This system may be achieved byselecting: C for M1 −0.007, Cx for m1 −0.0033, pitch of −45 degrees asp˜−0.5. A motivation to keep as much as possible the optics componentsaway from the work surface 1 as the work surface may be relatively in ahigh temperature when printing 3D metal parts as an example.

In another aspect of the invention it is necessary to have the first M1reflector 4 on the lower Z coordinates below the second M2 reflector 2.In this case the pitch of the first reflector 4 may be set to around49°. Increasing the angle will push the first M1 reflector 4 furtherback as in FIG. 26.

Although, Cx′ is a toric definition for a curve C (or any function sweptaround the y axis) that has an aspherical value Asp where asphericalvalue defines the departure from a sphere (asp for sphere is 0). Analternate definition and more elaborate can be used where Cx and Cy aredefined with their respective AspY and AspY spherical values. Thisdefinition has a higher degree of freedom as Cx can be an Aspheric aswell. When Cx,Cy and their respective aspherical values are calledbiconic surfaces, FIG. 8 shows a biconic construction performed onreflector M1 4. Additionally, Aspherical values can be defined inalternate ways as Shape where Shape=Asp+1. As Shape default value 1represents a sphere. Similarly or alternatively, a surface can bedefined with two orthogonal ellipses where their vertices meet at thesurface optical axis.

Yet, another aspect of the invention is using the same parabolacurvature for the first M1 reflector 4 and the second M2 reflector 2 asshown in FIG. 27 where the beam source 8 is located at the paraboloidfocal point and where the second matching surface reflecting aconverging beam to at the work surface 7 which is also the focal pointof the parabola where the distance between the first M1 reflector 4 andthe second M2 reflector 2 may be any distance because of the collimatedbeam between the surfaces. When the distance R 11 is selected then thesecond M2 reflector 2 ring is created by swapping around the parabolacurve at a distance R or curvature Cx′=1/R. In practicality, the secondM2 reflector surface 2 should be negative mathematically as the first M1reflector 4 faces the second M2 reflector 2 at all times. Additionally,the second M2 reflector surface 2 may be flipped vertically so the focuspoint will be away from the beam source 5 as it is shown in FIG. 28 andFIG. 17. This system is imposing distance 10 and 12 to be the same. Thisis an additional advantage in the assembly process where opticscalibration is mitigated compare to other systems as the same off Axisportion of the paraboloid facing the paraboloid focal point is selectedfor both M1 4 and M2 2 surfaces where the parabolic segment for M1 andM2 are matching.

Another aspect of the invention is to use a flat second M2 reflector 2(cone). Then, the first M1 reflector may comprise Biconic surfaces,where the curve Cx is aspheric and Cy is apheric as well. The followingparameters will produce the first M1 reflector 4, where the work surfaceradius may be 100 mm. Please note: the mm unit is not crucial. They canbe inches or any other units or multipliers when using multipliers thenall dimensions need to be corrected as shown earlier. FIG. 24 shows alayout of the system and FIG. 24B the resulting final beam. FIG. 13 alsoshows the diverging beam source shape and FIG. 14 the desired beam shapeand size at the work surface 7. FIG. 14 is the desired beam for allother samples in this document when dealing with expanding beams. Inthis instance the beam is expanding with Na of 0.15.

M1 with Cy=−0.00769 and Aspy=−0.8, Cx=−0.00451, Aspx=1, Pitch=45.4degrees will produce a focused output in the same as the source beam(105 um):

FIG. 24. shows the placement of M1, M2 and the beam source along the Zaxis measured in mm when the Origin is at the M2 vertex as follows:

-   -   Beam source Z coordinate 36 t: −57.7    -   Vertex cone at coordinate 37: 0 (origin)    -   M1 coordinate 27: 97.7    -   Work area at 28: 155.6

Accordingly, an object of the present invention is to address theoptical design of the components for handling the beam of the prior artby providing corrective elements, whereby the beam has the desireddimensions in the first and second direction when incident on the worksurface or when the beam keeps the proportion between the first andsecond directions when incident on the work surface.

1. A beam director comprising: a beam source rotatable about alongitudinal axis, an actuator for rotating the beam source about thelongitudinal axis, whereby the beam source rotates and reflects the beamat a constant angle to the longitudinal axis; an annular reflectorencircling the beam source coinciding with the longitudinal axis of therotating actuator; constantly facing the beam source at a constantangle; a second reflector including a reflective surface at an acuteangle to the longitudinal axis for reflecting the beam, configured toreflect the beam towards a work surface at a constant angle thereto; anda beam corrector comprising a reflective surface on the second reflectorfor modifying the beam dimensions; whereby when the beam is activatedand the actuator rotates the beam source, the beam strikes the reflectorrotating the beam and reflecting the beam to the work surface; the beamthen following a curved path relative to the work surface, tracing outan arc on the work surface; and wherein the beam corrector comprises areflective surface on the second reflector with curvature correction inthe first (x′) direction and in the second perpendicular direction (y′).2. A beam director comprising: a rotatable first reflector rotatableabout a longitudinal axis for receiving a beam from a beam source alongthe longitudinal axis, the first reflector including a reflectivesurface at an acute angle to the longitudinal axis for reflecting thebeam; an actuator for rotating the first reflector about thelongitudinal axis, whereby the first reflector rotates and reflects thebeam at a constant angle to the longitudinal axis; an annular secondreflector encircling the first reflector, a center of the firstreflector coincides with the longitudinal axis of the first reflector,constantly facing the first reflector at a constant angle; the secondreflector configured to reflect the beam towards a work surface at aconstant angle thereto; a beam corrector comprising a reflective surfaceon the second reflector for modifying the beam dimensions; whereby whenthe beam is activated and the actuator rotates the first reflector, thebeam strikes the rotating first reflector rotating the beam andreflecting the beam to the second reflector, which reflects the beam tothe work surface; the beam then following a curve path relative to thework surface, tracing out an arc on the work surface; wherein thereflective surface of the first and second reflectors changes the beamdimensions to a desired dimension in either a first (x′) direction or ina second perpendicular direction (y′) or in both; wherein the firstreflective surface comprises a lying on a first plane orthogonal to asecond curve lying on a second plane where the first and second planesare orthogonal and vertex's of the first and second curves meet at thelongitudinal axis. wherein the second reflector includes a toric surfacewhere the toric surface is a surface swept out when a function z(y) isrotated about an axis that is parallel to local y axis represented by:z(y)=C·y ²/(1+√{square root over (1−(Asph+1)·C ² ·y ²))}+A ₁ ·y+A ₂ ·y² + . . . +A ₁₄ ·y ¹⁴ wherein the function is rotated at a distance1/Cx′ where Cx′ is the reciprocal of the radius of the circle in the xzplane; wherein Asph is a value representing a departure from a sphereshape; wherein polynomials coefficients A_(j) for any j from 0 to 14 is0 when C is non zero or when C is zero then at least one of the A_(j)coefficient is non zero; wherein the polynomial coefficients provide ahigher degree of definition to the rotated function z(y); and where C isthe curvature defining the rotated function.
 3. The beam directoraccording to claim 1, wherein the second reflector comprises a toroidalsurface with curvature C1 in a first direction and curvature C2 in asecond perpendicular direction; wherein the beam source is a distance dfrom a toroidal origin and rotatable along the C1 surface; and whereinthe longitudinal axis is parallel with a toroidal vertical axis
 4. Thebeam director according to claim 2 wherein the first mirror comprises arotating flat mirror at an acute angle of 45 degrees from thelongitudinal axis, and wherein the beam source is positioned along thelongitudinal axis, whereby the beam source directs the beam to the firstreflector and the first reflector reflects the beam to the toroidalsurface, whereby, the beam is activated according to the equations:C ₁ C ₂ +d=R cos θR−r+d=R cos θ  (4) where the second mirror comprises a toroidal surfacewhere V is the toroidal vertex where C1 is the first center of a firsttoroidal with a radius R′ laying on the zy plane where C2 is a secondcenter for a second toroidal radius r′ laying on the xy plane where thebeam source is perpendicular to a line connecting C1,V and C2 where thebeam source optical axis is on C2 where the beam is reflected from thefirst reflector striking at the second reflector at M2 of the Toroidalsurface and in a distance d from the source optical axis where q is thedistance from the second reflector M2 to a point I at the work surfacewhere q=d+h and the angle in the triangle M2 C1 V is θ R′ is calculatedby: $\begin{matrix}{{R^{\prime} - {R^{\prime}\cos^{2}\theta} + d} = {\left. {R^{\prime}\cos\;\theta}\Rightarrow R^{\prime} \right. = \frac{d}{{\cos\;\theta} - {\sin^{2}\theta}}}} & (5)\end{matrix}$ and r′ is calculated by:1/R′ cos θ=cos θ/r′⇒r′=R′ cos²θ  (2)
 5. The beam director according toclaim 2, wherein the second reflector comprises a paraboloid surface,and wherein the first reflector comprises a biconic surface, wherein afirst surface comprises a spherical surface, and an orthogonal secondcurved surface with an aspherical surface value between 0 and −1, andpitch in about 45 degrees.
 6. The beam director according to claim 2,wherein the first reflector is a biconic surface comprises a sphericalsurface, and a second surface comprising an aspherical surface, andwherein the aspherical surface and the spherical surface meet at avertex.
 7. The beam director according to claim 2, wherein the secondreflector is configured to focus the beam only in one direction; andwherein the one direction is used to construct a logical pixel.
 8. Thebeam director according to claim 2, wherein the first reflectorcomprises a first paraboloid surface, and second spherical plane whereinthe second reflector comprise a second paraboloid surface; and whereinthe first surface is pitched at about 45 degrees. wherein the vertex ofthe first reflector is facing an off-axis portion of the secondreflector at around P where P is the second reflector focal point on theparaboloid plane.
 9. The beam director according to claim 8, wherein thefirst reflector paraboloid surface is substantially identical to thesecond reflector paraboloid surface.
 10. The beam director according toclaim 2, wherein the second reflector comprises a conical surface,wherein the first reflector comprises a biconic surface; wherein a firstcurvature of a first biconic surface is about twice a second curvatureof a second biconic surface; and wherein the aspherical value for thefirst biconic surface is about −0.8 wherein the aspherical value for thesecond surface is about 1 wherein the first reflector is pitched in anacute angle −45 degrees.
 11. A beam director comprising: a rotatablefirst reflector rotatable about a longitudinal axis for receiving a beamfrom a beam source along the longitudinal axis, the first reflectorincluding a reflective surface at an acute angle to the longitudinalaxis for reflecting the beam; an actuator for rotating the firstreflector about the longitudinal axis, whereby the first reflectorrotates and reflects the beam at a constant angle to the longitudinalaxis; an annular second reflector encircling the first reflector, acenter of the first reflector coincides with the longitudinal axis ofthe first reflector, constantly facing the first reflector at a constantangle; the second reflector configured to reflect the beam towards awork surface at a constant angle thereto; a beam corrector comprising areflective surface on the second reflector for modifying the beamdimensions; whereby when the beam is activated and the actuator rotatesthe first reflector, the beam strikes the rotating first reflectorrotating the beam and reflecting the beam to the second reflector, whichreflects the beam to the work surface; the beam then following a curvepath relative to the work surface, tracing out an arc on the worksurface; wherein the reflective surface of the first and secondreflectors changes the beam dimensions to a desired dimension in a first(x′) direction and in a second perpendicular direction (y′); wherein thefirst reflective surface comprises a biconic surface where the firstcurve is lying on a first plane orthogonal to a second curve lying on asecond plane where the first and second planes are orthogonal andvertex's of the first and second curves meet at the longitudinal axis.wherein the second reflector includes a toric surface where the toricsurface is a surface swept out when a function z(y) is rotated about anaxis that is parallel to local y axis represented by z(y)
 12. The beamdirector according to claim 11, wherein the second reflector comprises aparaboloid surface z(y), and wherein the first reflector comprises abiconic surface, wherein a first plane curve comprises a sphericalsurface, and an orthogonal second plane curve comprises a surface withan aspherical value between 0 and −1, and pitch in about 45 degrees. 13.The beam director according to claim 11, wherein the second reflector isconfigured to focus the beam only in one direction; and wherein the onedirection is used to construct a logical pixel where the logical beamsize is controlled by the beam speed.
 14. The beam director according toclaim 2, wherein the second reflector comprises a conical surface,wherein the second reflector is configured to focus the beam only in onedirection; and wherein the one direction is used to construct a logicalpixel, where the logical beam size is controlled by the beam speed. 15.The beam director according to claim 12, wherein the vertex of the firstreflector is facing an off-axis portion of the second reflector ataround P where P is the second reflector focal point on the paraboloidplane.
 16. The beam director according to claim 11, wherein the firstreflector paraboloid surface is substantially identical to the secondreflector paraboloid surface.
 17. The beam director according to claim11, wherein the first reflector comprises a first paraboloid surface,and second spherical plane, wherein the second reflector comprise a conesurface; and wherein the first surface is pitched at about 45 degrees.wherein the vertex of the first reflector is facing an off-axis portionof the second reflector at around P where P is the second reflectorfocal point on the paraboloid plane.
 18. The beam director according toclaim 11, wherein the first reflective surface comprises a firstspherical curve lying on a first plane orthogonal to a second paraboliccurve lying on a second plane where the first and second planes areorthogonal and vertex's of the first and second curves meet at thelongitudinal axis.
 20. The beam director according to claim 11, whereinthe second reflector includes a toric surface where the toric surface iscomposed of a surface swept out at a distance Cx′ when a function z(y)=yis rotated about an axis that is parallel to the local y axis.
 21. Thebeam director according to claim 11, wherein the second reflectorincludes a tonic surface where the tonic surface is composed of asurface swept out at a distance Cx′ when a function z (y)=4*P*y² isrotated about an axis that is parallel to the local y axis; and whereinthe first reflector is positioned at about p distance from the vertex ofthe second reflector, where P is the focal point of the function. 22.The beam director according to claim 11, wherein the second reflectorincludes a tonic surface where the tonic surface is composed of asurface swept out at a distance Cx′ when a function z²+y²=r² rotatedabout an axis that is parallel to the local y axis. where r is theradius of the sphere surface.